I have a laptop running Windows XP that developed a stop error, so it never completes its load of Windows. I can't repair the problem with the recovery disks that came with the system without reformating the HDD. Frankly, I care less about getting the machine up and running and more about recovering some of the data files that I never backed up.

Could I manually copy these files to a thumb drive by booting up the machine in DOS, and using command line to copy the files from the the HDD to the thumb drive?

If your hard drive is not damaged, you should be able to do as you suggest.